Unable to accommodate any more (inhabitants or contents); full. Unfortunately, we're full up here at the moment—no vacancy. Don't worry, I made sure that the dog's water bowl was full up before we left.
Farlex Dictionary of Idioms. © 2015 Farlex, Inc, all rights reserved.
Rur. full. I ate till I was full up. I can't get any more gas in the tank. It's full up.
McGraw-Hill Dictionary of American Idioms and Phrasal Verbs. © 2002 by The McGraw-Hill Companies, Inc.